|
%I #20 May 26 2019 19:38:04
%S 3,5,7,11,23,47,59,83,107,167,179,227,239,263,347,359,383,467,479,503,
%T 563,587,719,839,863,887,983,1019,1187,1223,1283,1307,1319,1367,1439,
%U 1487,1523,1619,1823,1907,2027,2039,2063,2099,2207,2243,2447
%N a(1) = 3; a(n) is the smallest prime such that gcd(a(i)-1, a(n)-1) = 2 holds for 1 <= i < n.
%C a(n) exists for all n, which is easily shown by Dirichlet's theorem on arithmetic progressions.
%C Apart from 3, the first term that is not a term in A005385 is 239. The first term in A092307 and A119660 (apart from 2) that is not a term here is 443.
%C Clearly all safe primes are in this sequence, and all terms except a(2) = 5 are == 3 (mod 4).
%H Robert Israel, <a href="/A303705/b303705.txt">Table of n, a(n) for n = 1..10000</a>
%e a(13) = 239 since lcm(a(1)-1, a(2)-1, ..., a(12)-1) = 2^2*3*5*11*23*29*41*53*83*89*113 and 239-1 = 2*7*17.
%p A[1]:= 3: L:= 2:
%p for i from 2 to 100 do
%p p:= nextprime(A[i-1]);
%p while igcd(L, p-1) > 2 do p:= nextprime(p) od:
%p A[i]:= p;
%p L:= ilcm(L, p-1);
%p od:
%p seq(A[i],i=1..100); # _Robert Israel_, Apr 29 2018
%Y Cf. A005385, A079148, A092307, A119660.
%K nonn
%O 1,1
%A _Jianing Song_, Apr 29 2018
%E Corrected by _Robert Israel_, Apr 29 2018
|
